Evaluation and improvement of the regulatory inference for large co-expression networks with limited sample size

Abstract

BackgroundCo-expression has been widely used to identify novel regulatory relationships using high throughput measurements, such as microarray and RNA-seq data. Evaluation studies on co-expression network analysis methods mostly focus on networks of small or medium size of up to a few hundred nodes. For large networks, simulated expression data usually consist of hundreds or thousands of profiles with different perturbations or knock-outs, which is uncommon in real experiments due to their cost and the amount of work required. Thus, the performances of co-expression network analysis methods on large co-expression networks consisting of a few thousand nodes, with only a small number of profiles with a single perturbation, which more accurately reflect normal experimental conditions, are generally uncharacterized and unknown.MethodsWe proposed a novel network inference methods based on Relevance Low order Partial Correlation (RLowPC). RLowPC method uses a two-step approach to select on the high-confidence edges first by reducing the search space by only picking the top ranked genes from an intial partial correlation analysis and, then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association.ResultsWe selected six co-expression-based methods with good performance in evaluation studies from the literature: Partial correlation, PCIT, ARACNE, MRNET, MRNETB and CLR. The evaluation of these methods was carried out on simulated time-series data with various network sizes ranging from 100 to 3000 nodes. Simulation results show low precision and recall for all of the above methods for large networks with a small number of expression profiles. We improved the inference significantly by refinement of the top weighted edges in the pre-inferred partial correlation networks using RLowPC. We found improved performance by partitioning large networks into smaller co-expressed modules when assessing the method performance within these modules.ConclusionsThe evaluation results show that current methods suffer from low precision and recall for large co-expression networks where only a small number of profiles are available. The proposed RLowPC method effectively reduces the indirect edges predicted as regulatory relationships and increases the precision of top ranked predictions. Partitioning large networks into smaller highly co-expressed modules also helps to improve the performance of network inference methods.The RLowPC R package for network construction, refinement and evaluation is available at GitHub: https://github.com/wyguo/RLowPC.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-017-0440-2) contains supplementary material, which is available to authorized users.

Improving network inference algorithms using resampling methods

“…Thus far, we have focused on this application using a set of known transcription factor-target pairs to assess performance, as done in DREAM5. However, network inference methods can also be used to determine functional overlap from transcriptional (or other) data across many conditions [ 4 , 17 , 21 , 22 ]. Thus, we wanted to assess the ability of bootstrapped inference methods to infer edges between genes in the same pathways.…”

“…Guo et al 2017 employed use of partial correlations (i.e. isolation of a single gene pair at a time), extracting only the most highly correlated relationships as edges in their RLowPC (Relevance Low order Partial Correlation) method [ 17 ]. Friedman et al 1999 applied bootstrapping to yield a successful result, but by resampling genes, not conditions, and applying to small, synthetic datasets [ 14 ].…”

Dynamic Bayesian Network Learning to Infer Sparse Models From Time Series Gene Expression Data

“…One reasons for this poor performance is that in DREAM4 networks, there are gene clusters with highly cohesive expression patterns. All pairs of such a cluster have high correlations between them that can result in a large number of indirect edges in the learned networks [75]. Another reason is that the DREAM4 networks are even sparser than the AR(1) models, the five 100 gene networks have an average of 2.31% arcs in the network.…”

“…For evaluation, we use the same metrics as mentioned in Section 3.5.1. However, following [75], we evaluated learned networks based on undirected network structures. This is because our methods do not incorporate perturbation information as prior knowledge.…”

DNA Methylation Network Estimation with Sparse Latent Gaussian Graphical Model

“…Most studies that do use methylation data estimate networks by directly correlating all CpG site pairs, with a focus on module detection [2][3][4][5][6]. However, the typical small sample-tovariable ratio limits the accuracy of the resulting networks [7]. Also, interpreting methylation networks is more difficult, since less is known about the functional role and gene targets of non-coding regulatory regions.…”